The authors apply the technique of conditional nonlinear optimal perturbations （CNOPs） as a means of providing initial perturbations for ensemble forecasting by using a barotropic quasi-geostrophic （QG） model in a...The authors apply the technique of conditional nonlinear optimal perturbations （CNOPs） as a means of providing initial perturbations for ensemble forecasting by using a barotropic quasi-geostrophic （QG） model in a perfect-model scenario. Ensemble forecasts for the medium range （14 days） are made from the initial states perturbed by CNOPs and singular vectors （SVs）. 13 different cases have been chosen when analysis error is a kind of fast growing error. Our experiments show that the introduction of CNOP provides better forecast skill than the SV method. Moreover, the spread-skill relationship reveals that the ensemble samples in which the first SV is replaced by CNOP appear superior to those obtained by SVs from day 6 to day 14. Rank diagrams are adopted to compare the new method with the SV approach. The results illustrate that the introduction of CNOP has higher reliability for medium-range ensemble forecasts.展开更多
We establish Talagrand＇s T2-transportation inequalities for infinite dimensional dissipative diffusions with sharp constants, through Galerkin type＇s approximations and the known results in the finite dimensional ca...We establish Talagrand＇s T2-transportation inequalities for infinite dimensional dissipative diffusions with sharp constants, through Galerkin type＇s approximations and the known results in the finite dimensional case. Furthermore in the additive noise case we prove also logarithmic Sobolev inequalities with sharp constants. Applications to Reaction- Diffusion equations are provided.展开更多
We show large deviation expansions for sums of independent and bounded from above random variables. Our moderate deviation expansions are similar to those of Cram′er(1938), Bahadur and Ranga Rao(1960), and Sakhanenko...We show large deviation expansions for sums of independent and bounded from above random variables. Our moderate deviation expansions are similar to those of Cram′er(1938), Bahadur and Ranga Rao(1960), and Sakhanenko(1991). In particular, our results extend Talagrand's inequality from bounded random variables to random variables having finite(2 + δ)-th moments, where δ∈(0, 1]. As a consequence,we obtain an improvement of Hoeffding's inequality. Applications to linear regression, self-normalized large deviations and t-statistic are also discussed.展开更多
By using a split argument due to[1],the transportation cost inequality is established on the free path space of Markov processes.The general result is applied to stochastic reaction diffusion equations with random ini...By using a split argument due to[1],the transportation cost inequality is established on the free path space of Markov processes.The general result is applied to stochastic reaction diffusion equations with random initial values.展开更多
基金supported by State Key Laboratory of Severe Weather, Chinese Academy of Meteorological Sciences Program for Basic Research of China (No. 2008LASWZI01)the Chinese Academy of Sciences (Grant No. KZCX3-SW-230)the National Natural Science Foundation of China (Grant No. 40675030)
文摘The authors apply the technique of conditional nonlinear optimal perturbations （CNOPs） as a means of providing initial perturbations for ensemble forecasting by using a barotropic quasi-geostrophic （QG） model in a perfect-model scenario. Ensemble forecasts for the medium range （14 days） are made from the initial states perturbed by CNOPs and singular vectors （SVs）. 13 different cases have been chosen when analysis error is a kind of fast growing error. Our experiments show that the introduction of CNOP provides better forecast skill than the SV method. Moreover, the spread-skill relationship reveals that the ensemble samples in which the first SV is replaced by CNOP appear superior to those obtained by SVs from day 6 to day 14. Rank diagrams are adopted to compare the new method with the SV approach. The results illustrate that the introduction of CNOP has higher reliability for medium-range ensemble forecasts.
基金Project supported by the Yangtze Scholarship Program
文摘We establish Talagrand＇s T2-transportation inequalities for infinite dimensional dissipative diffusions with sharp constants, through Galerkin type＇s approximations and the known results in the finite dimensional case. Furthermore in the additive noise case we prove also logarithmic Sobolev inequalities with sharp constants. Applications to Reaction- Diffusion equations are provided.
基金supported by National Natural Science Foundation of China (Grant Nos. 11601375 and 11626250)
文摘We show large deviation expansions for sums of independent and bounded from above random variables. Our moderate deviation expansions are similar to those of Cram′er(1938), Bahadur and Ranga Rao(1960), and Sakhanenko(1991). In particular, our results extend Talagrand's inequality from bounded random variables to random variables having finite(2 + δ)-th moments, where δ∈(0, 1]. As a consequence,we obtain an improvement of Hoeffding's inequality. Applications to linear regression, self-normalized large deviations and t-statistic are also discussed.
基金supported by National Natural Science Foundation of China(11671372,11771326,11831014).
文摘By using a split argument due to[1],the transportation cost inequality is established on the free path space of Markov processes.The general result is applied to stochastic reaction diffusion equations with random initial values.
